Difference Between State Function and Path Function Explained

The Difference Between State Function And Path Function is a classic concept in thermodynamics and physical chemistry, crucial for JEE Main exams. Grasping this difference helps you solve problems related to thermodynamic properties, heat, work, and process calculations. Think of a mountain: the height (altitude) is the same no matter how you climb, but the distance and effort vary with the route. Similarly, some properties depend only on the state, while others depend on the path taken.

Understanding State Function: Definition & Key Examples

State functions are properties whose values depend only on the current equilibrium state of the system, not on the process or path taken to reach that state. Mathematically, a state function can be represented as a change ∆F, such that ∆F = F_final – F_initial, regardless of the transformation path.

• Examples: Internal energy (U), pressure (P), temperature (T), volume (V), enthalpy (H), entropy (S).
• Typical units: For enthalpy, J (joules); for pressure, Pa (pascals); for entropy, J/K.
• In a PV diagram, any state function is fixed by a single point.
• If you return to the starting state via any process, net change in a state function is zero.

Decoding Path Function: Concept & Classic Cases

Path functions are properties whose magnitude depends on the specific path taken between two states, not just on the states themselves. They are not point properties but process-dependent quantities, commonly denoted by inexact differentials (e.g., δQ for heat, δW for work).

• Examples: Heat (Q), work (W), frictional loss.
• Units: Both heat and work are measured in joules (J).
• Different processes between same states yield different values of path functions.
• Illustrated by the area under the curve on a PV diagram (for work).

Tabular Comparison: Difference Between State Function And Path Function

This table helps you quickly memorise the main differences for MCQs and short-answer sections in JEE exams. Use it for last-minute revision or whenever you get confused about “state function vs path function”.

Visualising State and Path Functions in Thermodynamics

Visualise the difference between state function and path function using a PV diagram. Imagine moving from state A to state B along two different paths (say, one straight, one curved). Internal energy change (∆U) is the same for both, but work done (area under the curve) differs as each path encloses a different area.

Real-life analogy: Climbing a hill, the height gained is a state function; calories burned depend on the path, a path function.

Exam Context: Identifying State Function and Path Function in JEE Numericals

In a typical JEE Main question, you might be asked: “Which of the following is a state function? (a) Internal energy (b) Work (c) Heat (d) Both (a) and (b)”. The correct answer is Internal energy; both heat and work are path functions.

• State functions: Identify by checking if the property is independent of the actual process.
• Path functions: Check if different processes between the same states alter the value.
• Shortcut: Changes in state functions in a cyclic process are zero.
• Exam tip: For calculations involving heat and work, specify process (isothermal, adiabatic, etc.).

Common Errors & Memory Aids For State Vs Path Functions

A frequent mistake in JEE is assuming heat and work are state functions just because they appear in the first law of thermodynamics. In fact, internal energy is a state function, but heat and work are path functions; their values depend on how energy is transferred, not just on the start and end states.

• If a property is “stored” in the system (e.g., energy, entropy), it is likely a state function.
• If a property describes “exchange” during a process (e.g., heat, work), it's a path function.
• Remember: ∆U or ∆H for a cyclic process is 0, but net Q and net W may not be zero.

Cheat Sheet: Key Distinctions & Revision Points

• State functions: U, H, S, P, V, T; path functions: Q, W, frictional energy loss.
• State function → value fixed by initial and final state only.
• Path function → value depends on how you go from start to end.
• In diagrams, state functions are point properties; path functions are “areas” (process dependent).
• Understand the laws of thermodynamics for applications.

For further practice and advanced concepts, explore resources such as thermodynamics overview, detailed notes on enthalpy and internal energy, and process numericals in heat and work in thermodynamics. Vedantu’s subject experts ensure each explanation is exam-focused and cross-checked with the latest JEE Main syllabus.